The influence of the place-value structure of the Arabic number ...

As already mentioned in the introduction the only other neural network model
accounting for the whole range of two-digit numbers is the one by Grossberg and Repin
(2003). Please note that Grossberg and Repin (2003) postulate the origin of the representation
of multi-digit numbers within their model to be driven by verbal number words. This means,
that their model was not explicitly organized along place-value constraints but assumed that
apart from a primary number line coding single-digit numbers (but not being necessarily
limited to these) so-called number categories associated with verbal markers (such as e.g., the
suffix -ty) form the basis for the representation of multi-digit numbers. Thereby, the number
categories should be more or less language specific as e.g., the Basque number word system
inherits a combination of base-20 and base-10 properties. Nevertheless, although their model
seemed to produce compatibility like effects (cf. Figure 23, p. 1130) the authors did not
evaluate these systematically and neither did they interpret these effects in terms of placevalue
integration as proposed by the current study. Taken together, the model by Grossberg
and Repin (2003) should also be capable of accounting for the compatibility effect as long as
the number words used for training the model retain the base-10 place-value structure of the
Arabic number system.
Finally, another aspect of input format apart from the number word dependency in the
Grossberg and Repin (2003) model may be worth considering. As the separation of tens and
units is only possible in symbolic numerical notations but not in non-symbolic notation (e.g.,
dot pattern) decomposed processing of tens and units may be limited to symbolic
presentations. On the other hand, the representation of overall magnitude is not tied to
symbolic notation that closely. Thereof, the question arises whether the representation of
overall magnitude is mandatorily symbolic and linear as well – an issue discussed in the
following section.
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